Tunneling conductance of a two-dimensional electron gas with Rashba spin-orbit coupling

We theoretically studied the in-plane tunneling spectroscopy of the hybrid structure composed of a metal and a two-dimensional electron gas with Rashba spin-orbit coupling. We found that the energy spacing between two distinct features in the conductance spectrum can be used to directly measure the Rashba energy. We also considered the effect that varying the probability of spin-conserving and spin-flip scattering at the interface has on the overall conductance. Surprisingly, an increase in interface scattering probability can actually result in increased conductance under certain conditions. Particularly, in the tunneling regime, an increase in spin-flip scattering probability enhances the conductance. It is also found that the interfacial scattering greatly affects the spin polarization of the conductance in metal, but hardly affects that in the Rashba system.

Figure 1

The top sketches are the energy contours of the electron in the metal (left) and the Rashba system (right). The angles $\theta$ and $\phi$ are defined as those between the $x$ axis and the momenta of electrons in the metal and the Rashba system, respectively. The dashed line that crosses both sides shows the momentum states with the same $k_z$. The dotted line is the line of the maximum value of $k_z$, which defines the maximum incident angle ${\theta }_m$. The lower sketches are the corresponding energy spectra ($E$ vs the magnitude of momentum). $E_F$ and $E_0$ are the metal Fermi energy and the off-set energy of the Rashba system, respectively.

Figure 2

(Color online) The plot on the left is the conductance spectrum in the case where the energy band of the Rashba system is partly occupied $\left(E_0=-0.075E_F\right)$ and on the right is the plot in the case where the band is unoccupied $\left(E_0=0.05E_F\right)$. The derivative of the conductance spectrum on the right $\left(dG/dV\right)$ is shown in the inset. $Z$ and $Z_F$ are set equal to zero. $m/m^{\ast }=10$ and $k_0=0.05q_F$.

Figure 3

(Color online) Differential conductance spectra $G$ for different $Z_F$ in the case where (a) $Z=0$, (b) $Z=0.5$, and (c) $Z=2.0$.

Figure 4

Differential conductance $G\left(eV\right)$ plotted as a function of the spin-flip barrier height $Z_F$ at a constant energy $eV$ slightly below [upper panel, denoted by $G^{<}\left(Z_F\right)$] and slightly above [lower panel, denoted by $G^{>}\left(Z_F\right)$] the energy corresponding to the crossing of the Rashba-split bands. The arrows indicate the values of $Z_F^{\ast }$, where the maximum differential conductances $G^{>}$ and $G^{<}$ occur, for $Z=1.0$ (thick arrows) and 2.0 (dashed-dotted arrows).

Figure 5

The plots of the spin polarization of the conductance in metal and RS as a function of energy when $Z$ is (a) 0 and (b) 0.5.

Figure 6

Density of states of each branch of the 2DEG with the Rashba spin-orbit coupling. The contour plots on the left and on the right are those in the case where $E<E_0$ and $E>E_0$, respectively. When $E>E_0$, the outer contour is that of $-$ branch and the inner one is that of $+$ branch. When $E<E_0$, both energy contours belong to the $-$ branch. The arrows represent the spin direction of the states with positive $v_x$.